"""
    util/odds.py

    Calculate the odds of winning a lottery game
"""

from math import comb


def calculate_odds(pool_size: int, draw_count: int) -> int:
    """
    Calculate the total number of possible combinations in a set of numbers with a specific draw count.

    :param pool_size: Total count of numbers in the pool
    :param draw_count: The count of numbers to draw from the pool
    :return: The total number of possible combinations

    Example:
        If a lottery game has a main ball pool of 49 numbers from which 5 numbers are drawn and a pool of
        18 numbers from which 1 number is drawn (game ball), calculate the odds of winning that game.

        >>> calculate_odds(pool_size=49, draw_count=5)
        1906884
        >>> calculate_odds(pool_size=18, draw_count=1)
        18
    """

    if draw_count < 0 or draw_count > pool_size:
        raise ValueError('Integer values must be positive and draw counts must be less than pool size.')
    total_combinations = comb(pool_size, draw_count)
    return total_combinations


def get_odds_of_winning(
        main_ball_draw_pool: int,
        main_ball_draw_count: int,
        game_ball_draw_pool: int,
        game_ball_draw_count: int
) -> str:
    """
        Calculate the odds of winning a specific lottery game with one draw

        :param main_ball_draw_pool: Total count of numbers in the main ball pool
        :param main_ball_draw_count: The count of numbers to draw from the main ball pool
        :param game_ball_draw_pool: Total count of numbers in the game ball pool
        :param game_ball_draw_count: The count of numbers to draw from the game ball pool

        :return: The odds of winning a specific lottery game with one draw

        Example:
            To calculate the odds of winning a lottery game with 5 numbers drawn from a main ball pool of 49 and
            1 number drawn from a game ball pool of 19 numbers.

            >>> get_odds_of_winning(main_ball_draw_pool=49, main_ball_draw_count=5, game_ball_draw_pool=18, game_ball_draw_count=1)
            'The odds of winning are 1 in 34,323,912'
    """

    if (main_ball_draw_count < 0 or main_ball_draw_count > main_ball_draw_pool or
            game_ball_draw_count < 0 or game_ball_draw_count > game_ball_draw_pool):
        raise ValueError('Integer values must be positive and draw counts must be less than pool size.')

    main_ball_odds = calculate_odds(main_ball_draw_pool, main_ball_draw_count)
    game_ball_odds = calculate_odds(game_ball_draw_pool, game_ball_draw_count)

    return f"The odds of winning are 1 in {main_ball_odds * game_ball_odds:,}"